A set B of vectors in a vector space V is called a '''basis''' if every element of V may be written in a unique way as a '''finite linear combination of elements''' of B.
The coefficients of this linear combination are referred to as '''components or coordinates of the vector''' with respect to B.
The elements of a basis are called '''basis vectors'''.
Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.[1] In other words, a basis is a linearly independent spanning set.
A vector space can have several bases; however all the bases have the same number of elements, called the dimension of the vector space.
A set B of vectors in a vector space V is called a basis if every element of V may be written in a unique way as a finite linear combination of elements of B.
The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B.
The elements of a basis are called basis vectors.
Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.[1] In other words, a basis is a linearly independent spanning set.
A vector space can have several bases; however all the bases have the same number of elements, called the dimension of the vector space.
span
basis of a vector
linearly dependent
linearly independent